Temporal variation in transmission during the COVID-19 outbreak in Italy
S. Abbott (1), J. D. Munday (1), J. Hellewell (1), R. N. Thompson (1), N. Bosse (1), CMMID COVID team (1), S. Flasche (1), A. J. Kucharski (1), R. M. Eggo (1), S. Funk (1).
Correspondence to: sam.abbott@lshtm.ac.uk
1. Center for the Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London WC1E 7HT, United Kingdom
Last Updated: 2020-03-15
Note: this is preliminary analysis, has not yet been peer-reviewed and is updated daily as new data becomes available. This work is licensed under a Creative Commons Attribution 4.0 International License. A summary of this report can be downloaded here
Summary
Aim: To identify changes in the reproduction number, rate of spread, and doubling time during the course of the COVID-19 outbreak in Italy whilst accounting for potential biases due to delays in case reporting.
Latest estimates as of the 2020-03-15
Map
Summary of latest reproduction number and case count estimates
Figure 2: Cases with date of onset on the day of report generation and the time-varying estimate of the effective reproduction number (bar = 95% credible interval) based on data from the 2020-03-15. Countries/Regions are ordered by the number of expected daily cases and shaded based on the expected change in daily cases. The dotted line indicates the target value of 1 for the effective reproduction no. required for control and a single case required fror elimination.
Reproduction numbers over time in the six countries with the most cases currently
Figure 3: Time-varying estimate of the effective reproduction number (light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range) based on data from the 2020-03-15 in the countries/regions expected to have the highest number of incident cases. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence. The dotted line indicates the target value of 1 for the effective reproduction no. required for control.
Latest estimates summary table
| Country/Region | Cases with date of onset on the day of report generation | Expected change in daily cases | Effective reproduction no. | Doubling time (days) |
|---|---|---|---|---|
| National | 1486 – 10286 | Increasing | 1.3 – 2.5 | 3.4 – Cases decreasing |
| Lombardia | 580 – 4156 | Increasing | 1.2 – 2.2 | 3.9 – Cases decreasing |
| Emilia Romagna | 178 – 1254 | Increasing | 1.3 – 2.3 | 2.9 – Cases decreasing |
| Piemonte | 89 – 702 | Increasing | 1.3 – 2.6 | 2.2 – Cases decreasing |
| Veneto | 103 – 684 | Increasing | 1.2 – 2.4 | 3.6 – Cases decreasing |
| Marche | 98 – 646 | Increasing | 1.4 – 3 | 2.4 – 17 |
| P.a. Trento | 52 – 515 | Increasing | 1.9 – 6 | 1.2 – Cases decreasing |
| Toscana | 44 – 417 | Increasing | 1.4 – 3.1 | 2.1 – Cases decreasing |
| Liguria | 31 – 278 | Increasing | 1.3 – 3.3 | 2.7 – Cases decreasing |
| Lazio | 26 – 239 | Increasing | 1.4 – 3.3 | 1.9 – 7.1 |
| Puglia | 20 – 193 | Increasing | 1.5 – 3.7 | 1.8 – 8.2 |
| Campania | 21 – 184 | Increasing | 1.3 – 2.8 | 2 – Cases decreasing |
| Friuli Venezia Giulia | 12 – 143 | Increasing | 1.2 – 2.8 | 2.6 – Cases decreasing |
| P.a. Bolzano | 8 – 114 | Increasing | 1.2 – 3.6 | 0.19 – Cases decreasing |
| Sardegna | 8 – 108 | Increasing | 1.4 – 4.1 | 0.37 – Cases decreasing |
| Umbria | 8 – 106 | Increasing | 1.5 – 4 | 1.6 – 10 |
| Sicilia | 8 – 104 | Increasing | 1.2 – 2.7 | 1.7 – Cases decreasing |
| Abruzzo | 4 – 79 | Increasing | 1.2 – 3.2 | 1.7 – Cases decreasing |
| Valle D’aosta | 2 – 54 | Increasing | 1.3 – 4.1 | 0.35 – Cases decreasing |
| Calabria | 1 – 38 | Increasing | 1.3 – 3.6 | 0.19 – Cases decreasing |
| Basilicata | 1 – 20 | Unsure | 0.5 – 3.8 | 0.13 – Cases decreasing |
| Molise | 1 – 20 | Unsure | 0.2 – 2.7 | 0.15 – Cases decreasing |
Table 1: Latest estimates of the number of cases by date of onset, the effective reproduction number, and the doubling time for the 2020-03-15 in each region included in the analysis. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate. China excludes Hubei.
Methods
Summary
- Case counts by date, stratified by import status (local or imported), were constructed using the World Health Organization (WHO) situation reports and partial line-lists for each region [1,2].
- Case onset dates were estimated using case counts by date of report and a distribution of reporting delays fitted to partial line-lists from each region considered where available.
- Censoring of cases was adjusted for by assuming that the number of cases is drawn from a binomial distribution.
- Time-varying effective reproduction estimates were made with a 7-day sliding window using EpiEstim [4,5] adjusted for imported cases and assuming an uncertain serial interval with a mean of 4.7 days (95% CrI: 3.7, 6.0) and a standard deviation of 2.9 days (95% CrI: 1.9, 4.9) [6].
- Time-varying estimates of the doubling time were made with a 7-day sliding window by iteratively fitting an exponential regression model.
Limitations
- The estimated onset dates are based on current data for the delay in reporting. These data may not be representative of the underlying reporting distribution.
- The estimate of not-yet-confirmed cases to scale up recent numbers is uncertain and relies on the observed delays to confirmation to remain constant over the course of the outbreak.
- All data used is at a national/regional level; diagnostic capabilities may vary in different parts of each country/region, adding uncertainty to the reported numbers.
- Trends identified using our approach are robust to under-reporting assuming it is constant but absolute values may be biased by reporting rates. Pronouced changes in reporting rates may also impact the trends identified.
- Data on imported cases was only partially available.
- The reporting delay could not be estimated from line-list data for all regions. Region specific details are given in the individual regional reports.
- Data on imported cases may not be fully complete. This may bias estimates upwards when overall case counts are low.
Detail
Data
We used partial line-lists from each region that contained the date of symptom onset, date of confirmation and import status (imported or local) for each case [3] where available. The region reports give details of the steps taken where this data were not available. Daily case counts by date of report were extracted from the World Health Organization (WHO) situation reports for every location considered [1,2]. The case counts (and partial line-lists where available) were used to assemble the daily number of local and imported cases. Where the partial line-lists and case counts disagreed, it was assumed that the partial line-lists were correct and the WHO case counts were adjusted so that the overall number of cases occurring remained the same but the number of local cases being adjusted as needed.
Adjusting for reporting delays
Reporting delays for each country were estimated using the corresponding partial line-list of cases. The reporting delay could not be estimated from line-list data for all regions. Region specific details are given in the individual regional reports. The estimated reporting delay was assumed to remain constant over time in each location. We fitted an exponential distribution adjusted for censoring [7] to the observed delays using stan [8]. We then took 1000 samples from the posterior distribution of the rate parameter for the exponential delay distribution and constructed a distribution of possible onset dates for each case based on their reporting date. To prevent spuriously long reporting delays, we re-sampled delays that were greater than the maximum observed delay in the observed data.
To account for censoring, i.e. cases that have not yet been confirmed but will show up in the data at a later time, we randomly sampled the true number of cases (including those not yet confirmed) assuming that the reported number of cases is drawn from a binomial distribution, where each case has independent probability \(p_i\) of having been confirmed, \(i\) is the number of days of the symptom onset before the report maximum observed report delay, and \(p_i\) is the cumulative distribution of cases that are confirmed by day \(i\) after they develop symptoms. We did not account for potential reporting biases that might occur due to changes in the growth rate of the outbreak over time.
Statistical analysis
We used the inferred number of cases to estimate the reproduction number on each day using the EpiEstim R package [4]. This uses a combination of the serial interval distribution and the number of observed cases to estimate the reproduction number at each time point [10,11], which were then smoothed using a 7-day time window. We assumed that the serial interval was uncertain with a mean of 4.7 days (95% CrI: 3.7, 6.0) and a standard deviation of 2.9 days (95% CrI: 1.9, 4.9) [6]. We used a common prior for the reproduction number with mean 2.6 and a standard deviation of 2 (inflated from 0.5 found in the reference) [12]. Where data was available, we used EpiEstim to adjust for imported cases [5]. The expected change in daily cases was defined using the proportion of samples with a reproduction number less than 1 (subcritical). It was assumed that if less than 5% of samples were subcritical then an increase in cases was definite, if less than 20% of samples were subcritical then an increase in cases was likely, if more than 80% of samples were subcritical then a decrease in cases was likely and if more than 95% of samples were subcritical then a decrease in cases was definite. For countries/regions with between 20% and 80% of samples being subcritical we could not make a statement about the likely change in cases (defined as unsure).
We estimated the rate of spread (\(r\)) using linear regression with time as the only exposure and logged cases as the outcome for the overall course of the outbreak [13]. The adjusted R^2 value was then used to assess the goodness of fit. In order to account for potential changes in the rate of spread over the course of the outbreak we used a 7-day sliding window to produce time-varying estimates of the rate of spread and the adjusted R^2. The doubling time was then estimated using \(\text{ln}(2) \frac{1}{r}\) for each estimate of the rate of spread.
We report the 95% confidence intervals for all measures using the 2.5% and 97.5% quantiles. The analysis was conducted independently for all regions and is updated daily as new data becomes available. Confidence in our estimates is shown using the proportion of data that were derived using binomial upscaling.
Regional reports
National
Summary
Figure 4: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 1486 – 10286 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 2.5 |
| Rate of spread | -0.022 – 0.21 |
| Doubling time (days) | 3.4 – Cases decreasing |
| Adjusted R-squared | -0.14 – 0.97 |
Table 4: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 5: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Lombardia
Summary
Figure 7: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 580 – 4156 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 2.2 |
| Rate of spread | -0.064 – 0.18 |
| Doubling time (days) | 3.9 – Cases decreasing |
| Adjusted R-squared | -0.17 – 0.93 |
Table 5: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 8: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Emilia Romagna
Summary
Figure 10: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 178 – 1254 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 2.3 |
| Rate of spread | -0.077 – 0.24 |
| Doubling time (days) | 2.9 – Cases decreasing |
| Adjusted R-squared | -0.19 – 0.97 |
Table 6: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 11: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Piemonte
Summary
Figure 13: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 89 – 702 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 2.6 |
| Rate of spread | -0.043 – 0.31 |
| Doubling time (days) | 2.2 – Cases decreasing |
| Adjusted R-squared | -0.15 – 0.9 |
Table 7: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 14: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Veneto
Summary
Figure 16: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 103 – 684 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 2.4 |
| Rate of spread | -0.16 – 0.19 |
| Doubling time (days) | 3.6 – Cases decreasing |
| Adjusted R-squared | -0.25 – 0.87 |
Table 8: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 17: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Marche
Summary
Figure 19: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 98 – 646 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.4 – 3 |
| Rate of spread | 0.042 – 0.29 |
| Doubling time (days) | 2.4 – 17 |
| Adjusted R-squared | 0.15 – 0.99 |
Table 9: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 20: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
P.a. Trento
Summary
Figure 22: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 52 – 515 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.9 – 6 |
| Rate of spread | -0.035 – 0.59 |
| Doubling time (days) | 1.2 – Cases decreasing |
| Adjusted R-squared | -0.17 – 0.97 |
Table 10: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 23: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Toscana
Summary
Figure 25: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 44 – 417 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.4 – 3.1 |
| Rate of spread | -0.067 – 0.33 |
| Doubling time (days) | 2.1 – Cases decreasing |
| Adjusted R-squared | -0.18 – 0.97 |
Table 11: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 26: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Liguria
Summary
Figure 28: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 31 – 278 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 3.3 |
| Rate of spread | -0.098 – 0.26 |
| Doubling time (days) | 2.7 – Cases decreasing |
| Adjusted R-squared | -0.19 – 0.97 |
Table 12: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 29: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Lazio
Summary
Figure 31: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 26 – 239 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.4 – 3.3 |
| Rate of spread | 0.098 – 0.37 |
| Doubling time (days) | 1.9 – 7.1 |
| Adjusted R-squared | 0.51 – 0.98 |
Table 13: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 32: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Puglia
Summary
Figure 34: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 20 – 193 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.5 – 3.7 |
| Rate of spread | 0.084 – 0.38 |
| Doubling time (days) | 1.8 – 8.2 |
| Adjusted R-squared | 0.39 – 0.97 |
Table 14: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 35: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Campania
Summary
Figure 37: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 21 – 184 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 2.8 |
| Rate of spread | -0.12 – 0.34 |
| Doubling time (days) | 2 – Cases decreasing |
| Adjusted R-squared | -0.25 – 0.97 |
Table 15: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 38: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Friuli Venezia Giulia
Summary
Figure 40: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 12 – 143 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 2.8 |
| Rate of spread | -0.4 – 0.27 |
| Doubling time (days) | 2.6 – Cases decreasing |
| Adjusted R-squared | -0.44 – 0.88 |
Table 16: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 41: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
P.a. Bolzano
Summary
Figure 43: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 8 – 114 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 3.6 |
| Rate of spread | -0.043 – 3.6 |
| Doubling time (days) | 0.19 – Cases decreasing |
| Adjusted R-squared | -0.14 – 0.93 |
Table 17: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 44: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Sardegna
Summary
Figure 46: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 8 – 108 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.4 – 4.1 |
| Rate of spread | -0.23 – 1.9 |
| Doubling time (days) | 0.37 – Cases decreasing |
| Adjusted R-squared | -0.16 – 0.8 |
Table 18: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 47: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Umbria
Summary
Figure 49: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 8 – 106 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.5 – 4 |
| Rate of spread | 0.07 – 0.43 |
| Doubling time (days) | 1.6 – 10 |
| Adjusted R-squared | 0.22 – 0.95 |
Table 19: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 50: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Sicilia
Summary
Figure 52: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 8 – 104 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 2.7 |
| Rate of spread | -0.3 – 0.42 |
| Doubling time (days) | 1.7 – Cases decreasing |
| Adjusted R-squared | -0.47 – 0.93 |
Table 20: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 53: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Abruzzo
Summary
Figure 55: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 4 – 79 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.2 – 3.2 |
| Rate of spread | -0.11 – 0.4 |
| Doubling time (days) | 1.7 – Cases decreasing |
| Adjusted R-squared | -0.18 – 0.87 |
Table 21: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 56: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Valle D’aosta
Summary
Figure 58: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 2 – 54 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 4.1 |
| Rate of spread | -0.1 – 2 |
| Doubling time (days) | 0.35 – Cases decreasing |
| Adjusted R-squared | -0.14 – 0.88 |
Table 22: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 59: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Calabria
Summary
Figure 61: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 1 – 38 |
| Expected change in daily cases | Increasing |
| Effective reproduction no. | 1.3 – 3.6 |
| Rate of spread | -0.073 – 3.6 |
| Doubling time (days) | 0.19 – Cases decreasing |
| Adjusted R-squared | -0.15 – 0.91 |
Table 23: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 62: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Basilicata
Summary
Figure 64: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 1 – 20 |
| Expected change in daily cases | Unsure |
| Effective reproduction no. | 0.5 – 3.8 |
| Rate of spread | -3.9 – 5.5 |
| Doubling time (days) | 0.13 – Cases decreasing |
| Adjusted R-squared | -0.17 – 0.68 |
Table 24: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 65: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Molise
Summary
Figure 67: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-15. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Estimate | |
|---|---|
| Cases with date of onset on the day of report generation | 1 – 20 |
| Expected change in daily cases | Unsure |
| Effective reproduction no. | 0.2 – 2.7 |
| Rate of spread | -5.8 – 4.8 |
| Doubling time (days) | 0.15 – Cases decreasing |
| Adjusted R-squared | -0.24 – 0.69 |
Table 25: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-15. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.
Time-varying rate of spread and doubling time
Figure 68: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-15. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Implementation details
Updates
References
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